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The expression provided is \( 3x\sqrt{x} \), and we are asked to rewrite it in the form \( ax^n \), where \( a \) is a constant and \( n \) is a power.

### Steps:

1. Recall that \( \sqrt{x} \) can be rewritten as \( x^{\frac{1}{2}} \) using exponent notation.
   
   So, \( 3x\sqrt{x} = 3x \cdot x^{\frac{1}{2}} \).

2. Next, we apply the rule of exponents: \( x^m \cdot x^n = x^{m+n} \).
   
   Here, \( x \) has an implied exponent of 1. So, we add the exponents:
   \[
   3x \cdot x^{\frac{1}{2}} = 3x^{1 + \frac{1}{2}} = 3x^{\frac{3}{2}}.
   \]

Thus, the expression \( 3x\sqrt{x} \) in the form \( ax^n \) is:
\[
3x^{\frac{3}{2}}.
\]

Would you like further details on the exponent rules or any related concepts?

### Related Questions:
1. How do you multiply expressions with exponents?
2. What are the rules for fractional exponents?
3. How do you simplify radical expressions using exponents?
4. Can you convert \( x^{\frac{3}{2}} \) back to radical form?
5. How do you add or subtract expressions with exponents?

### Tip:
Remember that radicals can always be rewritten in exponent form. For example, \( \sqrt{x} = x^{1/2} \). This makes working with radicals much easier when performing algebraic operations.

Write the expression 3x√x in the form ax^n.

Learn how to convert the expression 3x√x into the form ax^n using exponent rules. This involves converting radicals into fractional exponents and applying basic exponent properties. Ideal for students in Grades 9-11 studying algebra.

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